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# Variance: Why the 2014 Eagles might be “better” but finish the same

The role of certainty in preseason projections.

Are the Eagles better this season than they were last season?

I haven't ventured a complete answer just yet; I still have a lot of stats to go through. However, I have stated quite explicitly that, from a pure roster perspective, I don't think the Eagles improved very much (and may actually have gotten worse). There's a problem with that statement, though. It's incomplete. Here's why:

When we talk about a team's "true" ability level, we're not really discussing discrete values. Although many pundits (i.e. anyone/everyone on ESPN) views season projections this way, it's a very bad method of forecasting. In reality, ex-ante (before each season), the best we can do is put together an expected performance distribution. In other words, before the season, we have no idea how many wins each team will produce. Beyond our inability to fully quantify all the known controllable variables, there's a HUGE degree of natural uncertainty (luck) in the game.

I touched on this a bit before last season. In making my projection for the Eagles, I gave a range of outcomes before settling on 9.1 (if I remember correctly) as the average. I ALSO explained that the Eagles were among the highest VARIANCE teams heading into last season. Put simply, the team, prior to last season, had perhaps the largest range of expected outcomes. So while I thought the team "should" win between 9 and 10 games, I also thought it was reasonably possible for them to go 4-12 or 12-4. Chip Kelly was a big reason for that range; he brought with him a very large degree of uncertainty. In hindsight, things works out generally as expected (at least on this site) and the Eagles finished with 10 wins. Note that, given the point differential, the Eagles "true" performance last year was 9.4 wins (via Pythagorean formula).

So why am I telling you this?

Well, if we think about each team's expected performance as a probabilistic distribution, then there are TWO main ways for the team to actually improve. Most clearly, a team can increase it's average win projection. For instance, it could sign multiple impact starters, or take a great prospect very high in the draft. Doing so might shift the teams entire distribution to the right, like so:

This is a graphic I used before the playoff game against the Saints. The X-axis is wins in this example. The values don't really matter. What matters is that the team has moved from left to right. Clearly, the blue distribution represents a better team. It's average performance is much higher.

BUT, there is another way to improve (several actually but we're focusing on the big ones), at least conceptually. A team can keep its average win projection the same, but decrease its expected variance. For example, the Eagles might still be looking at 9.1 wins this year, but the team's range may have decreased. That means our certainty increases.

Visually, it might look like this (again borrowing from this post from last season):

Notice the Cardinals; distribution is much narrower than the Eagles'. Pretend that both have the same average (i.e. move the Eagles to the right so it's centered on the Cardinals).

That's better. To borrow a finance concept, think of the distribution like a stock. Many analysts/investors use volatility (technically standard deviation, not variance, but for our purposes they're the same thing) as a proxy for risk. When looking at an investment, you have to look at both the expected return AND the risk associated with the investment. Here, you have to look at both the expected average win projection AND the range of potential outcomes.

It's important to note here that, assuming a symmetrical distribution, narrowing the range ALSO decreases upside while minimizing downside. Hence, sometimes it is better to have a wide distribution, like when you are a bad team. However, since there are diminishing returns at the top end of the distribution (a 10 win playoff team isn't much worse off than an 11 win playoff team), especially where the Eagles look to be headed (good enough to make the playoff but not good enough to challenge for a bye), a smaller range of outcomes is an improvement for the team.

Here's the important part:

While it's unclear whether or not the Eagles have shifted their distribution to the right (i.e. expect to win more than 9.4 games this year), it seems very likely that the team has narrowed its range of expected outcomes.

Chip Kelly is no longer huge unknown. Nick Foles expected performance is undoubtedly higher this year than Michael Vick's was before last season. Personnel-wise, the Eagles have made significant improvements below the starters on the depth chart. Obviously, injuries are a massive source of uncertainty. Although the Eagles have not added any impact starters (making it tough to increase projected wins), they have made the roster more robust, particularly on the defensive side of the ball.

So yes, the Eagles likely are better this year, if only in terms of uncertainty. Whether the team's average win projection has improved is a separate issue that I'll address over the next couple of weeks.